The ability of atomic, colloidal, and nanoparticles to self-organize into highly ordered crystalline structures makes the prediction of crystal structures in these systems an important challenge for science. The question itself is deceivingly simple: assuming that the underlying interaction between constituent particles is known, which crystal structures are stable. In this talk, I will describe a Monte Carlo simulation method [1] combined with a triangular tesselation method [2] to describe the surface of arbitrarily shaped particles that can be employed to predict close-packed crystal structures in colloidal hard-particle systems. I will show that particle shape alone can give rise to a wide variety of structures with unusual properties [3-6], e.g., photonic band gap structures by using mixtures of spheres and tetramers or highly diffusive crystals in the case of truncated cubes or binary hard-sphere mixtures. Finally, I will show that the number of possible structures can even be enlarged further by combining the choice of particle shape with external fields, like confinement [7].

Colloidal systems are capable of self-assembling into a wide variety of ordered structures, ranging from the simple to the exceedingly complex. Often, however, no such assembly occurs, and the system instead displays dynamical characteristics of glass-formation. Here, we computationally investigate assembly failure in a family of monodisperse, one-component systems, composed of colloidal particles of polyhedral shapes with no interactions aside from those of excluded volume. We study the role that local structure plays in dynamical arrest in these entropic systems, and find that assembly failure arises from an ``identity crisis” experienced on a local level and manifested in shape space.

Due to the great wealth of experimentally available particle shapes, efficient methods for predicting self-assembly are of paramount importance in soft matter. I will present recent advances in density functional theory that allow fast exploration of parameter space to be followed by more precise particle-resolved computer simulation techniques or experiments. We have been focusing on liquid crystal phases of hard particles so far, since these constitute stringent tests on our theory due to the small free energy differences between the phases involved. Comparison between the theory and particle-resolved simulations for spherocylinders and rod-like polyhedra shows that the theory predicts self-assembly of liquid crystals with the required accuracy for fast exploration. We find that the flat-topped, rod-like polyhedra exhibit a significantly more stable smectic phase than the archetypical spherocylinders. This subtle effect of the particle shape is well captured by the theory, which is promising for applications of the theory to other phases and other interaction potentials.

Improvements in the synthesis of colloids mean that a great variety of complex asphericalshapes have become an experimental reality. Motivated by the possibility of a wide range of new phases, computational studies address the particle shape dependence of the colloidal self-assembly process.

Tapered ellipsoids, reminiscent of "pear-shaped" particles, have not been realised in experiments yet. Previouscomputational studies showed, however, that these pear assemblies form bicontinuous cubic gyroid phases,similar to those famously found in various biological lipid bilayer systems.

Based on these methods, we investigate an earlier stage of this self-assembly, namely the formation ofstructures from a small number of pears in a 'bath' of hard spheres. We observe the formation of star-likemicellar structures. We perform Monte Carlo simulations with two different tapered particles, pears and tapered spherocylinders, and compare their capability to form these clusters. In addition we investigate systems where the micelles themselves form bigger, potentially cubic phases in a hierarchical fashion. These results will inform a deeper understanding of the formation of bicontinuous structures in nature and a notion of the similarities and differences between enthalpic and entropic self-assembly.

Aspherical colloidal particles were assembled in a reversible and tunable manner by means of dielectrophoresis (DEP). Spherical particles with single spherical cavities (referred as “dimples”) adopted lattices with non-closed packed cmm plane group symmetry and a packing fraction of 0.68 at low electric field strengths. With increasing electric field strength, the packing structure reverted to the entropically favored close-packed structure with p6m symmetry and a packing fraction of 0.90 typically observed for spherical colloids. Open packing structures were also achieved in systems comprising cubic hematite colloids with cylindrical arms protruding from each face, referred to as “hexapods”. Upon application of an electric field, perpendicular to the field direction, the arms of the hexapods prevented close packing. The presence of a magnetic field was found to anneal the hexapod crystals, decreasing the number of defects. The magnetic field could also be used to manipulate the orientation and packing structure of the crystals. These findings suggest that the interaction between external fields and aspherical colloidal geometries can be used to induced open-packed and tunable structures in two-dimensional crystals.

CNCs are materials of increasing interest because of their size, aspect ratio, stiffness, renewability, and liquid crystal (LC) ordering. CNCs self-assemble into LC phases above a critical concentration, which is dictated by particle size and surface properties. In this work, we study this transition by observing the interactions of CNCs across a range of concentrations using isothermal titration calorimetry (ITC). This technique allows us to take highly precise heat measurements from the interactions of very small sample volumes. Addition of electrolytes also has a pronounced effect on the suspension behavior: at low ionic strengths (0-10 mM), the electrostatic double layer is compressed and the effective particle size is reduced. With increasing ionic strength (>20 mM), the electrolytes destabilize the suspension by neutralizing the electrostatic repulsive forces and inducing aggregation. The nature of this transition is examined for different electrolytes and CNC concentrations, with ITC results for both liquid crystal transition and ionic strength effects being corroborated using rheology and polarized optical microscopy (POM). These techniques provide relevant microstructural information in the form of rheology, and the presence and extent of anisotropic domains.

Coarse-graining colloidal interactions usually assumes that multi-body effects can beneglected. However, recent research demonstrate that multibody effects in polymercoated particles are significant and can induce changes in expected crystal lattices.Herein, we revisit a very recent paper that we published on anisotropic potentialscalculated by spatial series of density fields around colloids. We show that thismethod can be extended to perform time evolution of the density field in a fashionakin to Carr-Parinello molecular dynamics. Inclusion of a non-zero temperatureinduces fluctuations. For isolated colloids, these fluctuations correspond to collectivenormal modes.

We perform numerical simulations to study jammed packings containing a variety of nonspherical particle shapes (e.g. dimers, circulo-lines, circulo-polygons, ellipses, and dumbbells) in two spatial dimensions. By analyzing these packings, we propose criteria that particle shapes must satisfy to give rise to hypostatic jammed packings, with fewer contacts than degrees of freedom using naive constraint counting arguments. We show the packing fraction $\phi$ and coordination number $z$ for jammed packings of the particle shapes under study. In particular, we find that $\phi$ and $z$ obey a master curve for different particle shapes when they are plotted as a function of the asphericity ${\cal A} = p^2/4\pi a$, where $p$ and $a$ are the perimeter and area of the particles. We also calculate the principal curvatures of the particle contact constraint surfaces in high-dimensional configuration space to identify specific contacts in packings of spherocylinders that allow them to be jammed, yet hypostatic.

We conduct experiments to observe the effects surfaces have on the internal packing structure of particles. To observe this, we run an experiment using cylindrical containers of different diameters, and rods of aspect ratios ranging from 4 to 32. We find that the rods packed into smaller cylindrical containers yielded lower volume fractions than in larger containers. Our results are extrapolated to an infinite container size, and the subsequent volume fraction decreases with increasing aspect ratios, in agreement with previous simulations. The results also suggest that the surface effect on internal packing decreases with aspect ratio as well. We also conduct a second series of experiments using vibration to more closely pack the containers. This results in denser packings as expected, and also changes the influence of the boundaries.

We study 3D rod packings in cylindrical containers with two sizes by a computed tomography scanner. The aspect ratio of our rods is 1:8. We observe rods pack to a higher volume fraction phi in the larger container, suggesting a strong influence of the walls on the packing. In both containers, we observe that particles pack isotropically in the bulk, but pack differently near the side and bottom boundaries. Near the bottom boundary, the rods lie flat against the container boundary and thus pack with a higher phi than the bulk. In contrast, rods are loosely packed near the side boundary. For both the bottom and side boundaries, the range of influence of the boundaries is shorter than a rod length. The differences between the bottom and side boundaries show that gravity plays an important role in the packing of rods in small containers.

We model the packing of rodlike particles in confined geometries. Simulations are optimized for parallel processing on a Graphics Processing Unit. Simulated particles are spherocylinders (cylinders with hemispherical end-caps) of aspect ratios ranging from 4 to 32. Infinitesimal particles are distributed at random in a cylindrical container and allowed to expand until they overlap. A conjugate gradient method is used to minimize the elastic potential energy that accompanies overlap, and the growth/minimization process continues until the energy can no longer be minimized to an infinitesimal value. We find the jamming packing fraction decreases as the container becomes small, and is consistent with the idea of a boundary layer of randomly packed particles. From simulations we extract the large-container asymptotic packing fraction Φ∞, the decrease in packing fraction within the boundary layer δΦ and the size of the boundary layer δL. We also characterize orientation in the boundary layer at the container wall, floor and ceiling.

We investigate the flow behavior of aspherical, granular particles inplanar-shear flow geometry using large-scale computersimulations. Specifically, we explore how grain shape and friction influencethe constitutive "mu-of-I" rheology. We find that over a spectrum of grainshapes, spanning spheres to cubes, particle friction affects the rheologicalcharacterization more so than particle shape. Whereas, for a given particlefriction coefficient, particle shape affects the value of the bulk, dynamicfriction or stress aniostropy. We characterize these different flow regimesusing a range of structural and flow parameters.